基于近端算法的DC规划解球面约束下四次型极小化问题

A Proximal DC Algorithm for Quartic Minimization Over the Sphere

对于球面约束下的四次型极小化问题,可使用DC(difference of convex)规划来求解。现基于近端算法对DC算法进行了一些改进,提出pDCA和aDCA两种算法,并证明了算法局部收敛以及收敛速度至少达到了次线性收敛。数值实验结果表明,与一般的DC算法和对称移位高阶幂法相比,在计算时间和解的最优性方面都得到了很大提升。

DC programming is one of the methods for quartic minimization over the sphere.In this paper,a method for quartic minimization over the sphere is DC programming.We This paper proposes two algorithms,i.e.,pDCA and aDCA,to improve the DC algorithm based on the proximal algorithm.and propose two algorithms,pDCA and aDCA.We It also proves that the local convergence,where the convergence speed of the algorithm reaches at least sublinear convergence.Numerical experimental results show that compared with both the general DC algorithm and the HOPM,pDCA and aDCA require less time and the optimality of the calculation solution has been improved.